# What is the mode of a square waveguide $TE_{11}$ that is deformed into a circle?

I am trying to solve the 2013 paper set by ISRO for electrical engineers. I want some help to solve Question no 17 is correct.

So I don't even know how to approach the problem, what will be the new deformed radius? will volume be conserved? Can I say $$\r = \frac{a}{\sqrt{\pi}}\$$

Dominant mode in rectangular waveguide is TE10 and in circular waveguide is TE11.

Rectangular to circular waveguide transition convert dominant TE10 mode of rectangular waveguide to TE11 dominant mode of circular waveguide and vice versa.

Square/Rectangular and circular waveguide are commonly used in antenna feed networks for dual-polarization systems.

• Their high degree of symmetry enables one to achieve homogenous propagation for both polarization modes. Truncation of the guide cross-section under this condition enables the realization of broadband components for antenna applications, mode conversion, and polarization discrimination.

• It was observed that a smooth taper from circular to rectangular waveguide preserves the modal structure of both guides. That is, a smooth transition from rectangular to circular waveguide can preserve their common reflection symmetries.